For the MgSO₄ crystallizer of Example 27.5, the expected growth rate is 0.055 cm/h for a 20-mesh crystal. If the supersaturation is about 3 percent and the mass transfer coefficient is twice that for a freely falling particle, what is the actual supersaturation at the crystal surface?

Example 27.5

A continuous vacuum crystallizer is fed with a 31 percent MgSO₄ solution. The equilibrium temperature of the magma in the crystallizer is 86°F (30°C), and the boiling point elevation of the solution is 2°F (1.11°C). A product magma containing 5 tons (4,536 kg) of MgSO₄·7H.O per hour is obtained. The volume ratio of solid to magma is 0.15; the densities of the crystals and mother liquor are 105 and 82.5 lb/nt³. respectively. What are the temperature of the feed, the feed rate, and the rate of evaporation?